Camera-trapping data analysis
We used the camera trap data to develop detection matrices based on the absence (= 0) and presence (= 1) of jaguar and each of the five prey species selected. Each column on the recording sheet represented an eight-day interval during which the cameras were active, and each row represented a unique camera trap station; double stations were listed as a single station. These detection histories were used to investigate the spatial interactions between the jaguar and each of the main potential prey detected in the co-occurrence modeling. The prey species included in the analysis were Pecari tajacu , Cuniculus paca ,Dasyprocta punctata , Mazama temama , and Mazama pandora . Prey species that did not present enough detections,Tayassu pecari and Dasypus novemcinctus , were excluded.
We used a single season, two-species model (MacKenzie et al ., 2004, 2006) with R-studio software and the R-presence library to estimate occupation (co-occurrence) and detection (co-detection) for each pair of species (jaguar and prey). The naive occupation, which reflects the proportion of cameras detecting a species in relation to the total number of cameras, is reported. Two population parameters, occupancy and detection, were estimated, which provide an estimate of the proportion of an area occupied by a species.
We established the jaguar as the dominant species (A) and prey (B) as the subordinate species and adopted the eight model parameters proposed by Richmond et al . (2010). For occupancy (psi or Ψ): 1) ΨA - probability of occupancy for species A; 2) ΨBA - probability of occupancy for species B if species A is present; 3) ΨBa - probability of occupancy for species B if species A is absent, and for detection (r or ɣ), 4) pA - probability of detection for species A if species B is absent; 5) pB - probability of detection for species B if species A is absent; 6) rA probability of detection for species A if both species are present; 7) rBA - probability of detection for species B if species A was detected and both species are present; and 8) rBa - probability of detection for species B if species A was not detected and both species are present. If species occur independently, that is, the occupation of one species does not depend on the other, then ΨBA = ΨBa. Similarly, detection of one species relative to the presence or absence of another can be determined; if the detection of the species occurs independently, then rBA = rBa. We also used the interaction factor (SIF) which indicates if the species of interest occur independently. The parameter nu (N), which is the occupation probability estimate (B|A)/probability (B|a), indicates if the jaguar and the prey species use the sites independently, and the parameter rho (P), which is the detection probability (rBA /probability rBa), indicates if the detection of the predator affects the detection of a prey since they both occupy a site. Nu and rho (SIF) values that equal one suggest species occur independently, but SIF values <1 suggest species coexist less frequently than if they were distributed independently (avoidance among the pair of species analyzed) and SIF values >1 suggest a tendency for species to occur more frequently than if they were distributed independently.
We used the Akaike model selection criterion (Akaike, 1973) to identify which of the three models (below) that best describes the data on the joint occurrence of each pair of species and assigned the following variable definitions: SP is the effect of the species; INT is the effect of the interaction on the presence of species B whether species A is present or not; INT_o is the detection level interaction when the occupation of one species changes the probability of detection of the other species; and INT_d, is the detection level interaction where the detection of one species changes the probability of detection of the other species on the same occasion of the sampling (i.e., eight-day period).
• Model 1: psi~SP + INT, p~SP + INT_o + SP:INT_o + INT_d [psi (SP P INT) p (SP P INT_o P SP T INT_o P INT_d)]. This is the most complete model with three parameters for occupancy (psi) and five parameters for detection. It assumes the probability of occupancy depends on the occupancy of A and the probability of occupancy of BA because ΨBA = ΨBa. It also assumes that detection depends on pA, rA, pB, rBA and rBa.
• Model 2: psi~SP, p~SP + INT_o + INT_d + SP:INT_o psi (SP) p (SP P INT_o P INT_d P SP T INT_o). Occupancy depends only on the species, and unlike model 1, assumes that species occupancy is independent. This implies ΨBA = ΨBa and is represented by the absence in the adjustment of the interaction term in the occupancy.
• Model 3: psi~SP + INT, p~SP + INT_o + SP:INT_o psi (SP P INT) p (SP P INT_o P SP T INT_o). Unlike model 1, it assumes that detection probabilities of species B do not depend on the detection of species A (i.e., rBA = rBa ).